Question

You notice that a stairwell railing is a parallelogram. In parallelogram RALS: AL​segment A L = 26.5 feet RI​segment R I = 5.3 feet AR​segment A R = 6.2 feet What is the area of parallelogram RALS? Use the given information to complete the worksheet.

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Answer 1

To find the area of a parallelogram, we need to multiply the base by the height. In this case, we need to find the height of the parallelogram.

We can see that segment AL and segment RI are both perpendicular to segment AR. Therefore, we can use either of them to find the height.

Let's use segment AL as our height. To find the length of segment L​S, we can use the Pythagorean theorem:

L​S² = A​R² - R​I²

L​S² = 6.2² - 5.3²

L​S² = 16.21

L​S = √16.21

L​S ≈ 4.02 feet

Now we can find the area of the parallelogram:

Area = base x height

Area = AL x LS

Area = 26.5 x 4.02

Area ≈ 106.23 square feet

Therefore, the area of parallelogram RALS is approximately 106.23 square feet.

Explanation: